In my travels to various countries here in Europe, I have noticed an interesting trend. It is not without exception, certainly, but has caught my eye enough times to have me start looking out for it.
In an "old" European country with a large proportion of visible minorities, the people you see in a position of authority are usually the title race.
I first noticed it in Sweden, then in Norway, Finland, Holland, the UK... countries where you walk down the street and see a huge variety of skin tones. (This opposed to Small Country, where the permanent black residents can be counted on the fingers of one very deformed hand.) Immigrants are often accused of living off welfare and not working, but that's a whole different problem and one which, I believe, gets solved over a generation or two.
I also don't believe that visible minorities are discouraged from going into law enforcement and similar disciplines. I do, however, believe that they tend not to care.
The job where I have found many minorities was that of bus driver. Naturally, it is the biased view of a traveller on a budget that tends to use the cheapest form of public transport to get from the airport/ferry terminal to the center of town. But it does make sense. Driving a bus requires a couple months of training; unlike driving a cab, you don't need to know the language particularly well; and in Western Europe, it's a heavily unionized job. Here in Small Country with its national obsession with the free market, the transport workers are really the last trade union with the strength to demand something, as opposed to pleading for it. So your average bus driver in a European capital is going to be paid fairly well.
On the other hand, the police is not somewhere you go for the money. There's a huge problem right now in Small Country with the rescue workers (firefighters basically, but tasked with anything outside the strict responsibility of the cops and ambulance guys). Basically they earn nothing. The typical salary is half the national average. It's better in other departments and certainly better in other countries, but the pattern is still there.
The people who patrol the streets, fight fires, work the customs desks at the airport, are all people who care about their homeland.
Again I repeat, there are plenty of exceptions. But the next time you fly to Stockholm, the first stereotypical Norseman you are likely to see will be the border guard spot-checking you for drugs once you get off the plane - rather than the flight attendant or the cabbie driving you to your hotel.
Finally, the point about immigrants being lazy. The most non-European place I have been to was Rotterdam. Admittedly not a touristy city. Over four days in a metropolis with a population that matches the entire Small Country and perhaps exceeds it, I saw maybe three people who looked like you'd expect the Dutch to look. The rest of them were Africans, southeast Asians, Arabs, Turks... you name it. I was told by the people I stayed with that it wasn't just me - Rotterdam was in fact a predominantly non-white city.
And yet, it is the biggest seaport in the world, serving shipments to and from all of Europe, essentially. Keeping up that status takes a lot of hard work.
Oh, and the first Dutch-looking person I saw on that trip? The ticket-taker on the train from Schiphol airport.